Solve for $x$ : $5x^2 + 55x + 150 = 0$
Explanation: Dividing both sides by $5$ gives: $ x^2 + {11}x + {30} = 0 $ The coefficient on the $x$ term is $11$ and the constant term is $30$ , so we need to find two numbers that add up to $11$ and multiply to $30$ The two numbers $5$ and $6$ satisfy both conditions: $ {5} + {6} = {11} $ $ {5} \times {6} = {30} $ $(x + {5}) (x + {6}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 5) (x + 6) = 0$ $x + 5 = 0$ or $x + 6 = 0$ Thus, $x = -5$ and $x = -6$ are the solutions.